Blenrig 5 Deform Cage isn't symmetrical
By the time I posted this question I'd already been fighting this problem for a day, but not being one to just sit around waiting for an answer, I kept looking around and trying things. 

This has something to do with the scaling. My original model was very large -more than 20x the size of the default Blenrig armature. When I scaled the model down to a size pretty close to the default rig size it all came out fine.

Since extensive searches on multiple boards yielded zero answers I figured I'd answer my own question here in case anyone else has the problem. If anyone comes up with any details about the scaling issue or a way to bypass that problem please let us know!